6533b83afe1ef96bd12a6f2a

RESEARCH PRODUCT

Spectral approach to D-bar problems

Christian KleinKenneth D.t-r Mclaughlin

subject

[ MATH ] Mathematics [math]Spectral approachInverse conductivity problemBar (music)General MathematicsElectrical-impedance tomographyFOS: Physical sciences2 dimensions010103 numerical & computational mathematics01 natural sciencesDiscrete systemsymbols.namesakeConvergence (routing)FOS: MathematicsApplied mathematicsUniquenessStewartson-ii equationsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]Electrical impedance tomographyReconstruction algorithmsNumerical-solutionMathematicsNonlinear Sciences - Exactly Solvable and Integrable SystemsApplied MathematicsNumerical Analysis (math.NA)Integral equation010101 applied mathematicsFourier transformsymbolsUniquenessExactly Solvable and Integrable Systems (nlin.SI)

description

We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.

yearjournalcountryeditionlanguage
2017-06-01
http://arxiv.org/abs/1508.02363